Cylinder Surface Area and Volume Calculator
Compute the volume, lateral area, or total surface area of solid, hollow, or open-top cylinders. Perfect for engineering, tank design, and packaging calculations.
About this calculator
A solid cylinder's volume is V = π × r² × h, where r is the base radius and h is the height. Its lateral (side) surface area is A_lateral = 2π × r × h, and total surface area (both circular ends included) is A_total = 2π × r × h + 2π × r² = 2π × r × (h + r). For an open-top cylinder, only one base is counted: A_total = 2π × r × h + π × r². For a hollow cylinder with inner radius r_i = r − wall_thickness, the volume of material is V = π × (r² − r_i²) × h. The total surface area of a hollow cylinder also includes two annular rings and the inner lateral surface. These formulas are used in fluid storage, pipe sizing, and manufacturing.
How to use
Consider a solid cylinder with radius r = 5 units and height h = 10 units. Volume: V = π × 5² × 10 = π × 250 ≈ 785.40 cubic units. Lateral area: A_lateral = 2π × 5 × 10 = 100π ≈ 314.16 square units. Total surface area: A_total = 2π × 5 × (10 + 5) = 2π × 75 = 150π ≈ 471.24 square units. Enter radius = 5, height = 10, select 'Solid' cylinder type, and choose 'Volume' or 'Surface Area' from the Calculate dropdown.
Frequently asked questions
How do you calculate the volume of a hollow cylinder given its outer radius and wall thickness?
For a hollow cylinder, compute the inner radius as r_i = r − wall_thickness, where r is the outer radius. The volume of material is V = π × (r² − r_i²) × h. For example, a pipe with outer radius 6 cm, wall thickness 1 cm, and height 20 cm has inner radius 5 cm and material volume V = π × (36 − 25) × 20 = 220π ≈ 691.15 cm³. This is the volume of the pipe wall itself, not the fluid it carries. The fluid capacity is simply π × r_i² × h.
What is the difference between lateral surface area and total surface area of a cylinder?
Lateral surface area covers only the curved side of the cylinder, calculated as 2π × r × h. It represents the area you would need to wrap a label around a can. Total surface area adds the areas of both circular ends: A_total = 2π × r × h + 2π × r². For an open-top container like a drinking glass, you include only one base, giving A_total = 2π × r × h + π × r². Knowing which surface area you need is important for accurate material estimation in manufacturing and packaging.
How do I find the height of a cylinder if I know its volume and radius?
Rearrange the volume formula V = π × r² × h to solve for height: h = V / (π × r²). For instance, if a cylinder has volume 1000 cubic centimeters and radius 5 cm, then h = 1000 / (π × 25) = 1000 / 78.54 ≈ 12.73 cm. This rearrangement is useful in engineering when designing tanks or pipes to hold a specific volume within a given footprint. The same approach applies to hollow cylinders by substituting the annular base area (π(r²−r_i²)) for the full base area.